I have trouble seeing much of a difference between Calvinism and deism, functionally. The Calvinist God created the world he created. End of story. How can the Calvinist God be meaningfully described as an "interventionist."
It seems hard for God to intervene in a universe where God knows how the future will unfold is because he predetermined that is the way the future would unfold. What is [he] intervening with, himself?
To some extent I think this is a semantic quibble, although it goes to deep questions concerning the nature of God and causality. Let's begin with some exposition:
i) In mainstream Calvinism, God subsists outside of time and space.
God has made a physical universe. The physical universe includes physical causes. Natural processes.
The physical universe is like an automated machine. It does whatever it was programmed to do, no more and no less. The same kind of cause will produce the same kind of effect.
That's, in part, what we mean by ordinary providence.
However, the created order is not confined to the physical dimension. There's mental causation. The created order includes finite minds. Some finite minds are discarnate agents (angels) while other finite minds are embodied agents (humans). In addition, reality includes the divine mind, which exists outside the created order.
Unlike physical processes, which are thoughtless, intelligent agents can exercise rational discretion. Moreover, intelligent agents can manipulate a natural process to produce a desired effect that's different than what the natural process would produce absent the intervention of an intelligent agent.
That can involve mundane things like technology, or supernatural events like miracles. There are basically two kinds of miracles:
a) Classic miracles which circumvent natural processes. In the case of a classic miracle, the effect is not the result of the antecedent state. Rather, it's discontinuous with prior conditions leading up to that event. It has a mental rather than physical cause. It's not the end-result of a preceding chain of events.
b) Coincidence miracles which utilize natural processes. A coincidence miracle is the coordinated result of independent chains of events converging for the benefit of a particular individual or group. It reflects the discriminating intention of a powerful agent.
ii) Deism asserts the uniformity of nature. The universe operates according to natural laws. Natural events are law-like in the sense of mechanical regularity. The same kinds of things always happen. A closed system. A seamless causal continuum.
According to the classic metaphor, we inhabit a clockwork universe. God made the watch, wound it, and set it. Thereafter it runs of its own accord. It requires no maintenance.
Deism regards a miracle as analogous to a mechanic on the night watch who must superintend the machinery in case of malfunction. The mechanic must repair it in case it breaks down.
Or to continue with the watchmaker metaphor, God must periodically rewind or reset the watch if it runs down, runs fast, or runs slow. But that makes God a poor designer. So goes the argument.
Deism makes no allowance for supernatural mental causation as an integral element in natural history.
iii) In theological discourse, "intervention" is a term of art. As I use the term, an interventionist God is a God who works miracles and answers prayer–to take two paradigm examples. A Deist God or noninterventionist deity is a God who does not work miracles or answer prayer.
Put another way, divine "intervention" is synonymous with God's ongoing involvement in natural history and especially human history. By contrast, a Deist God is uninvolved in the subsequent course of world history. His participation begins and ends with the initial act of creation. (In some versions of Deism, God will judge the wicked when they die).
There are critics of "interventionist" terminology. They think the terminology has misleading connotations. For instance:
Some biblical fundamentalists think of God as an engineer who designed and created species of animals and plants like a watchmaker designing a watch. Ironically, this God of the world machine has more to do with science than with the bible or traditional Christian doctrines. When the machine model of nature took hold in seventeenth-century science, a new image of God came into being as a supernatural engineer, a machine-maker separate from nature.
You don’t believe in this kind of God, and neither do I. In traditional Christian theology, God is not a kind of craftsman, or demiurge, who makes the world in the first place and then retires, leaving it to work automatically, except for occasional interventions when he arbitrarily suspends the laws of nature. God is not a demiurge, and not a meddler with machinery. According to the traditional understanding in Christian and other theologies, God is the ground of all being, the reason why there is something rather than nothing. He sustains the world in its existence from moment to moment, and is doing so now.
Problem: "miracle," as used in these controversies, is not a biblical category. The God of the Bible is not a normally absent God who sometimes "intervenes." This God is always present and active, often surprisingly so...The "closed continuum" of cause and effect is a modernist myth. The God who does not "intervene" from outside but is always present and active within the world, sometimes shockingly, may well have been thus active on this occasion.
In English theology, the easy-going pre-Enlightenment assumption that the world of creation gave reliably straightforward witness to a good creator (I cited Bishop Butler above; we might include writers like Joseph Addison, too) had been shaken to the core by the Lisbon earthquake of 1755, which as Susan Neiman has argued must be seen as one of the proximate causes at least of the Enlightenment revolution. That revolution attempted to solve the problem, as well as several others, by cutting God loose from the world, drawing on the old upstairs/downstairs world of English deism. Religion became the thing that people did with their solitude, a private, inner activity, a secret way of gaining access to the divine rather than either an invocation of the God within nature or a celebration of the kingdom coming on earth as in heaven. God became an absentee landlord who allowed the tenants pretty much free rein to explore and run the house the way they wanted, provided they checked in with him from time to time to pay the rent (in much middle Anglican worship until the last generation, taking up the collection has been the most overtly sacramental act) and reinforce some basic ground rules (the Ten Commandments, prominently displayed on church walls, and the expectation that bishops and clergy will ‘give a moral lead’ to society). As we know, the absentee landlord quite quickly became an absentee, as in Feuerbach, whom Robinson quotes to this effect (p. 50) without any sense that Feuerbach himself has been subjected to damaging critique.
My sympathy for his plight has grown over the years as I have lived within the continuing split-level world of much English piety. The word ‘miracle’ is a case in point. Most people, not least in the media, still think of it as meaning an action performed by a distant, remote deity reaching in to the world from outside—just as to many people, still, the word ‘God’ itself conjures up a basically deist image of that kind of a being. I know that in fact that word ‘supernatural’ has a longer history than this and that, for instance, mediaeval theologians were able to use it in such away that it did not carry the baggage of an implied deism or semi-deism  (by which I mean the view which, while sharing deism’s gap between God and the world, holds that from time to time this ‘God’ can and does ‘intervene’). But I continue to find that this model dominates UK theological discourse, particularly among those of, or near, Robinson’s generation. Thus, for instance, when I have written about Jesus’ mighty acts, or about the resurrection, I have often been heard to be affirming one kind of post-Enlightenment supernaturalism (with an ‘interventionist’ God) over against one kind of post-Enlightenment naturalism (with a ‘non-interventionist’ God), even though I have frequently and explicitly renounced precisely this distinction and the framework which facilitates it (to the consternation of my ‘supernaturalist’ friends).
iv) There's some truth to these criticisms, but they are confused.
a) In classical theism, God is an "outside agent." God exists apart from the creation. God exits apart from the space-time continuum.
b) There are different ways of making something. I can plant an orchard, then abandon the orchard. What the orchard will be like 50 years later has nothing to do with me, beyond my initial contribution. It will be very different than if I tended the orchard on a regular basis.
c) Compare that to a novelist. The novelist exists outside the story. Yet he's involved in every detail of the story. In one respect, he causes everything to happen, from start to finish. The novelist is responsible for everything that's said and done in the course of the story.
But in another respect, characters drive the course of events. Conversely, characters react to events. Characters within the story drive the plot. They influence other characters. And they themselves are influenced by their circumstances.
You have both primary and secondary causation.
d) Does the God of Calvinism "intervene"? Depends on what you mean. As I said at the outset, I define an interventionist God as a God who does things like working miracles and answering prayer. That's clearly consistent with Calvinism.
I don't define an interventionist God as a God who alternates between participation and detachment. Indeed, the usual rap against Calvinism is not that God is too remote, but that God is too involved. Critics of Calvinism think God ought to be more detached.
Freewill theists limit divine intervention. Too much intrusion would either infringe on human freedom or trivialize the consequences of free choices.
Clearly the Calvinist God doesn't intervene in the sense of acting at cross-purposes with his plan. But why should we define divine intervention in that way?
iv) There are, of course, freewill theists who think God intervenes in the sense that he has to jump in every so often to make midcourse corrections lest things get totally out of hand. But that's not how Calvinism uses the term.
The part I don't really get is that Calvinists insist it is vitally important to point out that God knows all the possible games of chess the two players could have theoretically played. I guess I agree that that is knowledge that God has, but why is that relevant? God knows that it is theoretically possible two people could sit down for chess and just move their knights back and forth over the same spaces until they die of old age. So what? Why does that matter? Like I said, I think the important thing is that God knows ahead of time what game of chess the two players will actually play and the game of chess they would have played if he had not intervened on white's 10th move.
It's relevant for God to have counterfactual knowledge since God must be in a position to know what the possibilities are in order to instantiate a particular set of possibilities in space and time. God made the world by selecting and combining some possibilities to the exclusion of other possibilities. It doesn't a blind draw.
It amounts to God predetermining every move and pretty much playing chess with himself. When he is intervening, he is intervening with himself because he created a person to act one way, but finds it necessary to nevertheless intervene in time to bring about his predetermined outcomes.
i) One limitation of the chess analogy is that ordinarily, chess pieces are unintelligent. If, however, the chess pieces were rational agents, then you'd have some pieces playing against other pieces. Indeed, the pieces on one side strategize with each other on how to defeat the other side, and vice versa. And as the game progresses, from their perspective (unlike God's), they adapt their strategy to the changing situation.
ii) The other problem is that Jeff is hung-up on a particular connotation of "intervention."
iii) In addition, a lot depends on the metaphor we use to illustrate the point. If, instead of chess, we use a novel, you could say the novelist is telling himself a story. If, however, the characters were real people, like sentient virtual characters, then they experience the story. They are an audience for the story, like stage actors.